Question

Prove sin(90-theta).cos(90-theta) =cot theta/1+cot2 theta

Answer 1

Answer:

Answer

As we know that,

sin(90

o

−θ)=cosθ, cos(90

o

−θ)=sinθ,

cosec(90

o

−θ)=secθ, cot(90

o

−θ)=tanθ,

sec(90

o

−θ)=cosecθ, tan(90

o

−θ)=cotθ

∴

cosec(90−θ)sin(90−θ)cot(90−θ)

cos(90−θ)sec(90−θ)tanθ

+

cotθ

tan(90−θ)

∴

sin(90−θ)

1

×sin(90−θ)×tanθ

sinθ×

cos(90−θ)

1

×tanθ

+

cotθ

cotθ

=

cosθ

1

×cosθ

sinθ×

sinθ

1

+1

=1+1=2

Hence, option C is correct.